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Characterization of almost perfect nonlinear functions in terms of subfunctions

  • Anastasiya A. Gorodilova EMAIL logo
Published/Copyright: August 22, 2016

Abstract

The paper is concerned with combinatorial description of almost perfect nonlinear functions (APN-functions). A complete characterization of n-place APN-functions in terms of (n − 1)-place subfunctions is obtained. An n-place function is shown to be an APN-function if and only if each of its (n − 1)-place subfunctions is either an APN-function or has the differential uniformity 4 and the admissibility conditions hold. A detailed characterization of 2, 3 or 4-place APN-functions is presented.


Originally published in Diskretnaya Matematika (2015) 27, №3, 3-16 (in Russian).


Award Identifier / Grant number: 15-07-01328

Funding statement: This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 15-07-01328) and the Programme of Support of Leading Scientific Schools of the President of the Russian Federation (grant no. NSh-1939.2014.1)

Acknowledgement

The author expresses her gratitude to I.,A. Kruglikov for his attentive reading of the manuscript and valuable advice.

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Received: 2015-7-28
Published Online: 2016-8-22
Published in Print: 2016-8-1

© 2016 Walter de Gruyter GmbH, Berlin/Boston

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